When two or more candle flames are fused by approaching them together, the resulting large flame often exhibits flickering, i.e., prolonged high-frequency oscillation in its size and luminance. In the present work, we investigate the collective behaviour of three-coupled candle flame oscillators in a triangular arrangement. The system showed four distinct types of syncronised modes as a consequence of spontaneous symmetry breaking. The modes obtained include the in-phase mode, the partial in-phase mode, the rotation mode, and an anomalous one called the "death" mode that causes a sudden stop of the flame oscillation followed by self-sustained stable combustion. We also clarified the correlation between the inter-flame distance and the frequency with which the modes occur.